Answer:
15 possible pairs of friends could be chosen in this way.
Step-by-step explanation:
Given : You have 6 friends who want to go to a concert with you, but you only have room in your car for 2 of them. To avoid accusations of favoritism, you have your friends draw straws: There are 4 long and 2 short straws, and the short straws win.
To find : How many possible pairs of friends could be chosen in this way?
Solution :
Total number of friends = 6
The space in the car is for 2 person.
Since, the order doesn't matter we have to choose 2 people out of 6 so we apply combination.
As There are 4 long and 2 short straws, and the short straws win.
i.e. that 2 friends were chosen.
So, Possible ways to find the pairs of friends is [tex]^6C_2[/tex]
Solving,
[tex]^6C_2=\frac{6!}{2!(6-2)!}[/tex]
[tex]^6C_2=\frac{6\times 5\times 4!}{2\times 1\times 4!}[/tex]
[tex]^6C_2=3\times 5[/tex]
[tex]^6C_2=15[/tex]
Therefore, 15 possible pairs of friends could be chosen in this way.
